Estimations of positive roots of polynomials
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XVII, Tome 373 (2009), pp. 280-289 Cet article a éte moissonné depuis la source Math-Net.Ru

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We obtain new estimations for the positive roots of univariate polynomials. We discuss their efficiency and study numerical and computational aspects. Bibl. – 12 titles.
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D. Ştefănescu; V. Gerdt; S. Yevlakov. Estimations of positive roots of polynomials. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XVII, Tome 373 (2009), pp. 280-289. http://geodesic.mathdoc.fr/item/ZNSL_2009_373_a16/

[1] S. A. Abramov, Lectures on Complexity of Algorithms, MCCME, 2008 (in Russian)

[2] A. Akritas, “Linear and Quadratic Complexity Bounds on the Values of the Positive Roots of Polynomials”, Univ. J. Comput. Sci., 15 (2009), 523–537 | MR | Zbl

[3] M. Fujiwara, “Über die obere Schranke des absoluten Betrages der Wurzeln einer algebraischen Gleichung”, Tôhoku Math. J., 10 (1916), 167–171 | Zbl

[4] J. B. Kioustelidis, “Bounds for positive roots of polynomials”, J. Comput. Appl. Math., 16 (1986), 241–244 | DOI | MR | Zbl

[5] T. Kojima, “On the limits of the roots of an algebraic equation”, Tôhoku Math. J., 11 (1917), 119–127 | Zbl

[6] J.-L. Lagrange, Traité de la résolution des équations numériques, Paris, 1798; Reprinted in ØE uvres, VIII, Gauthier-Villars, Paris, 1879

[7] M. Mignotte, D. Ştefănescu, On an estimation of polynomial roots by Lagrange, IRMA Strasbourg 025/2002, 2002, 17 pp.

[8] M. Mignotte, D. Ştefănescu, Polynomials – An algorithmic approach, Springer Verlag, 1999 | MR | Zbl

[9] D. Ştefănescu, “New Bounds for Positive Roots of Polynomials”, Univ. J. Comput. Sci., 11 (2005), 2125–2131 | MR | Zbl

[10] D. Ştefănescu, “Computation of Dominant Real Roots of Polynomials”, Prog. and Compt. Sotfware, 34 (2008), 69–74 | MR | Zbl

[11] V. Sharma, “Complexity of real root isolation sing continued fractions”, Theor. Comp. Sci., 409 (2008), 292–310 | DOI | MR | Zbl

[12] E. Tsigaridas, I. Emiris, “On the complexity of real root isolation using continued fractions”, Theor. Comp. Sci., 392 (2008), 158–173 | DOI | MR | Zbl